Study programme competencies |
Code
|
Study programme competences / results
|
A3 |
CE3 - Reconocer y analizar problemas físicos, químicos, matemáticos, biológicos en el ámbito de la Nanociencia y Nanotecnología, así como plantear respuestas o trabajos adecuados para su resolución, incluyendo el uso de fuentes bibliográficas. |
A7 |
CE7 - Interpretar los datos obtenidos mediante medidas experimentales y simulaciones, incluyendo el uso de herramientas informáticas, identificar su significado y relacionarlos con las teorías químicas, físicas o biológicas apropiadas. |
B2 |
CB2 - Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio |
B4 |
CB4 - Que los estudiantes puedan transmitir información, ideas, problemas y soluciones a un público tanto especializado como no especializado |
B5 |
CB5 - Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía |
B6 |
CG1 - Aprender a aprender |
B7 |
CG2 - Resolver problemas de forma efectiva. |
B8 |
CG3 - Aplicar un pensamiento crítico, lógico y creativo. |
B9 |
CG4 - Trabajar de forma autónoma con iniciativa. |
B10 |
CG5 - Trabajar de forma colaborativa. |
B11 |
CG6 - Comportarse con ética y responsabilidad social como ciudadano/a y como profesional. |
B12 |
CG7 - Comunicarse de manera efectiva en un entorno de trabajo. |
C3 |
CT3 - Utilizar las herramientas básicas de las tecnologías de la información y las comunicaciones (TIC) necesarias para el ejercicio de su profesión y para el aprendizaje a lo largo de su vida |
C7 |
CT7 - Desarrollar la capacidad de trabajar en equipos interdisciplinares o transdisciplinares, para ofrecer propuestas que contribuyan a un desarrollo sostenible ambiental, económico, político y social. |
C8 |
CT8 - Valorar la importancia que tiene la investigación, la innovación y el desarrollo tecnológico en el avance socioeconómico y cultural de la sociedad |
C9 |
CT9 - Tener la capacidad de gestionar tiempos y recursos: desarrollar planes, priorizar actividades, identificar las críticas, establecer plazos y cumplirlos |
Learning aims |
Learning outcomes |
Study programme competences / results |
Identify the different types of differential equations and problems associated with them. Especially those originating in nanoscience and nanotechnology |
A3 A7
|
B2 B4 B6 B7 B8 B9
|
C3 C9
|
Know and acquire fluency in the techniques to obtain analytical and numerical solutions of models based on ordinary differential equations |
A3 A7
|
B2 B4 B6 B7 B8 B9 B12
|
C7 C8 C9
|
Know and acquire fluency in the techniques to obtain analytical and numerical solutions of models based on partial differential equations |
A3
|
B2 B5 B10 B11
|
C3 C7 C8 C9
|
Have criteria to choose the most efficient analytical and numerical techniques for models of real problems, especially those related to nanoscience and nanotechnology. |
A3
|
B2 B4 B5 B6 B7 B8 B9 B10 B11 B12
|
C3 C7 C8 C9
|
Manage software tools that implement the methodologies studied and know how to analyze the results |
A3 A7
|
B2 B4 B5 B6 B7 B9 B10 B12
|
C3 C9
|
Contents |
Topic |
Sub-topic |
Unit 1: First order ordinary differential equations |
- Initial value problem
- Analytic resolution
- Mathematical models
- Numerical resolution: Explicit Euler, Implicit Euler, Heun, Runge-Kutta.
- Aplications |
Unit 2: Systems of differential equations |
- Systems of differential equations
- Analytic resoluiton
- Estability
- Mathematical models
- Numerical schemes: Explicit Euler, Implicit Euler, Heun, Runge-Kutta.
- Applications |
Unit 3: Second order ordinary differential equations
|
- Initial value problem.
- Analytic resolution. Laplace transform, Fourier transform.
- Mathematical models.
- Numerical resoltion
- Aplications
- Contour problems
- Analytic resolution.
- Numerical resolution. Finite difference method.
- Sturm-Liouville problems. Numerical approximation of eigenvalues and eigenfunctions
- Aplications |
Tema 4: Ecuacións en derivadas parciais. |
- Ecuación de transporte. Resolución analítica mediante o método de características. Resolución numérica mediante el esquema de Godunov.
- Ecuación do calor 1D. Resolución analítica mediante separación de variables. Resolución numérica por diferencias finitas.
- Ecuación de ondas 1D. Resolución analítica mediante separación de variables. Resolución numérica por diferencias finitas.
- Ecuación de Laplace e Poisson. Resolución analítica mediante separación de variables. Resolución numérica por diferencias finitas
- Ecuación de calor 2D. Resolución analítica mediante separación de variables. Resolución numérica por diferencias finitas.
- Ecuación de Schrödinger. Resolución analítica mediante separación de variables.. Resolución numérica por diferencias finitas.
- Aplicacións
|
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Guest lecture / keynote speech |
A3 B2 B4 B5 B6 B7 B11 C8 |
28 |
56 |
84 |
ICT practicals |
A3 A7 B2 B4 B10 C3 C7 C9 |
12 |
25 |
37 |
Problem solving |
A7 B8 B12 |
8 |
16 |
24 |
Mixed objective/subjective test |
B7 B9 C9 |
3 |
0 |
3 |
|
Personalized attention |
|
2 |
0 |
2 |
|
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies |
Methodologies |
Description |
Guest lecture / keynote speech |
Exhibition of the contents specified in the program of the subject, for which audiovisual media (tablet) will be used. |
ICT practicals |
Interactive practices in which relevant problems in the field of Science and Engineering will be solved, using Python programming language. |
Problem solving |
Sessions where relevant problems in the field of Science and Engineering will be presented, which will be solved both analytically and numerically. The student must be able to reach the solution of any problem using pencil and paper or alternatively using computer tools (using Python), and compare the results. |
Mixed objective/subjective test |
Development of issues and problems of the subject. |
Personalized attention |
Methodologies
|
Problem solving |
ICT practicals |
|
Description |
a) The diversity of the students and their training make it advisable to have personalized guidance, which could be carried out through tutorials.
b) Practices with ITC tools in problem solving, or teachers will help students to develop two stated problems, as well as applications to problems in the field of Science and Engineering.
c) The specific personalized attention measures for "Students with recognition of part-time dedication and academic waiver of attendance exemption" for the study of the subject, the continuous evaluation of the practices through ITC and the resolution of problems carried out through tests online partials. |
|
Assessment |
Methodologies
|
Competencies / Results |
Description
|
Qualification
|
Mixed objective/subjective test |
B7 B9 C9 |
Test that includes the resolution of questions and problems of the subject (by hand and/or Python) |
50 |
Problem solving |
A7 B8 B12 |
Rosolution of practical problems |
25 |
ICT practicals |
A3 A7 B2 B4 B10 C3 C7 C9 |
Resolution of practical problems using the Python programming language |
25 |
|
Assessment comments |
The final qualification of the subject consists of three parts: - Qualification of internships through ICT (CP): between 0 and 2.5 points
- Problem Solving Qualification (CR): between 0 and 2.5 points
- Mixed test qualification (CE): between 0 and 5 points.
The final qualification will be the sum of three parts: Final_Note= CP + CR + CE, if the qualification of the mixed test (CE) is greater than 1.3 (over 5 points). In other case, the final qualification will be the mark obtained on the mixed test, CE. The qualifications of practices through ICT (CR) and problem solving (CP) will be retained in the second opportunity of the evaluation. Students who do not show up for the final mixed test will be considered as "Not presented". Observations on o “Students with recognition of part-time dedication and academic exemption from attendance exemption”: As specific personalized attention measures for o “Students with recognition of part-time dedication and academic exemption from attendance exemption” for or study da matter, the continuous assessment of the practices through ICT and the resolution of problems will be carried out through online partial tests.
|
Sources of information |
Basic
|
Richard G. Rice, Duong D. Do (2012). Applied Mathematics And Modeling For Chemical Engineers (2º ed). John Wiley & Sons
Wei-Chau Xie (2014). Differential Equations for Engineers (2º ed). Cambridge University Press
Stephen Lynch (2018). Dynamical Systems with Applications using Python. Springer
Dennis G. Zill (2018). Ecuaciones diferenciales con problemas con valores en la frontera (9ª ed). Cengage
C. Henry Edwards, David E. Penney (2017). Ecuaciones diferenciales y problemas con valores en la frontera. Cómputo y modelado (4ª ed). Pearson Education
William E. Boyce, Richard C. DiPrima, Douglas B. Meade (2017). Elementary Differential Equations and Boundary Value Problems, (11ª Ed). Willey |
|
Complementary
|
George F. Simmons (2016). Differential Equations with Applications and Historical Notes. Chapman and Hall/
William E. Boyce, Richard C. DiPrima, Douglas B. Meade (2017). Elementary Differential Equations and Boundary Value Problems, Student Solutions Manual, (11ª Ed). Wiley
Steven C. Chapra , Raymond P. Canale (2015). Métodos Nméricos para Ingenieros (7ª ed). McGraw-Hill
J. C. Butcher (2016). Numerical Methods for Ordinary Differential Equations, (3ª ed). Wiley
Svein LingeHans Petter Langtangen (2017). Programming for Computations - Python A Gentle Introduction to Numerical Simulations with Python. Springer |
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Recommendations |
Subjects that it is recommended to have taken before |
Numerical and Statistical Methods/610G04013 | Physics: Electricity and Magnetism/610G04007 | Fundamentals of Mathematics/610G04001 | Advanced Calculus /610G04009 | Physics: Mechanics and Waves/610G04002 | Fundamentals of Computing Science/610G04010 |
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Subjects that are recommended to be taken simultaneously |
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Subjects that continue the syllabus |
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Other comments |
Estudio diario dos contidos tratados na aula, complementándoos coa bibliografía recomendada. Para axudar a conseguir unha contorna inmediata sustentable e cumprir co punto 6 da "Declaración Ambiental da Facultade de Ciencias (2020)", os traballos documentais que se realicen nesta materia: Solicitaranse maioritariamente en formato virtual e soporte informático.
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